Finite Group Databasebeta

← #13169198

Subgroups — #13169198

Order 1728.

1668 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89018C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3#11723696C211yesmaximal, characteristic, complemented
4#11723517C211yesmaximal, characteristic, complemented
5#11723516C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723030C212yesmaximal, complemented
9#11722963C212yesmaximal, complemented
10#11722961C212yesmaximal, complemented
11#11722933C212yesmaximal, complemented
12#10595410—31nomaximal
13#10595007—31nomaximal
14#10593902—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6295C2212yes—
21C2×#6292C2212yes—
22C2×#6292C2212yes—
23C2×#6292C2212yes—
24C2×#6291C2212yes—
25C2×#6289C2212yes—
26#89018—24no—
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2212yes—
29C2×C3×#624C2212yes—
30C3×#3799—24no—
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C32×C4×Dic3C2211yescharacteristic
33#88814C2212yes—
34#88804C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2211yescharacteristic
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×#3832—31no—
41C2×C3×#239—31no—
42C2×C3×#235—31no—
43C2×#3799—31no—
44C2×#3799—31no—
45C2×#3799—61no—
46C2×#3799D311yescharacteristic, complemented
47#64139—31no—
48#64083—31no—
49C3×Q8×Dic3—31no—
50C3×C4×#67—31no—
51C3×C4×D12—31no—
52C3×C4×Dic6—31no—
53#63979—32no—
54#63958—32no—
55#63916—31no—
56#63916—32no—
57#63911—32no—
58#63911—32no—
59#63911—31no—
60#63911—31no—
61#63911—61no—
62#63910—32no—
63#63910—32no—
64#63909—31no—
65#63909—31no—
66#63909—31no—
67#63909—32no—
68#63909—61no—
69#63908—31no—
70#63906—32no—
71#63904—32no—
72C4×#626—32no—
73C4×#626D311yescharacteristic, complemented
74#63894—32no—
75Dic3×Dic6D311yescharacteristic, complemented
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C32×D3C2311yescharacteristic
80C2×C33×C4C2311yescharacteristic
81C4⋊(C3⋊(C3⋊D3))—22no—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4⋊(C3⋊D3)—22no—
85C3×C4×C3⋊D3—22no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C32×C4×D3—22no—
91C32×Dic6D414yescomplemented
92#6295—42no—
93#6292—24no—
94#6292—24no—
95#6292—42no—
96#6291—42no—
97#6289—24no—
98C3×#626—24no—
99C3×#626—22no—
100C3×#624—24no—
101#5834—91no—
102#5577—91no—
103#5553—91no—
104C2×C32×Q8—31no—
105C22×C32×C4—31no—
106C2×#638—32no—
107#3832—64no—
108C2×C4⋊(C3⋊D3)—32no—
109C2×C4⋊(C3⋊D3)—32no—
110C2×C4⋊(C3⋊D3)—31no—
111C2×C4⋊(C3⋊D3)—31no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—32no—
114C2×C4⋊(C3⋊D3)—61no—
115C2×C4⋊(C3⋊D3)—61no—
116C2×C4⋊(C3⋊D3)—61no—
117C2×C4⋊(C3⋊D3)—121no—
118C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
119C2×C4×C3⋊D3—32no—
120C2×C4×C3⋊D3C2×D311yescharacteristic
121C2×C3×#67—31no—
122C2×C3×#67—32no—
123C3×#239—64no—
124C3×#235—64no—
125C2×C3×D12—32no—
126C2×C3×D12—31no—
127C2×C3×D12—31no—
128C2×C3×D12—31no—
129C2×C3×D12—61no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—32no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3—61no—
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×Dic6—21no—
139C2×C3×Dic6C2×D311yescharacteristic
140C2×C3×Dic6C2×D311yescharacteristic
141C2×#626—32no—
142C2×#626—32no—
143C2×#626—32no—
144C2×#626—32no—
145C2×#626—32no—
146C2×#626—32no—
147C2×#626—32no—
148C2×#626—32no—
149C2×#626—32no—
150C2×#626—32no—
151C2×#626—62no—
152C2×#626—62no—
153C2×#626—62no—
154C2×#626—62no—
155C2×#626C2×D312yes—
156C2×#626C2×D311yescharacteristic
157C2×#625—32no—
158C2×#624—32no—
159C2×#624—32no—
160C2×#624—62no—
161C2×#624C2×D312yes—
162#3799—24no—
163#3799—68no—
164#3799—64no—
165#3799—64no—
166C32×C42—31no—
167#3752—32no—
168C4⋊(C3⋊Dic3)C2×D311yescharacteristic
169C3×#217—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—32no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—61no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—32no—
180C3×C4×Dic3—21no—
181C3×C4×Dic3—32no—
182C3×C4×Dic3—32no—
183C3×C4×Dic3C2×D311yescharacteristic
184C3×C4×Dic3C2×D311yescharacteristic
185Dic3⋊Dic3C2×D312yes—
186Dic3⋊Dic3C2×D311yescharacteristic
187#3722—32no—
188#3722—32no—
189#3722—32no—
190#3722—62no—
191#3722C2×D311yescharacteristic
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3C2×D311yescharacteristic
195Dic32C2×D312yes—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—22no—
198C2×C3⋊(C3⋊D3)—22no—
199C2×C3⋊(C3⋊D3)—22no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—22no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3C2×D414yes—
215C32×Dic3#4112yescomplemented
216C2×C3×#41—91no—
217C2×#239—31no—
218C2×#239—91no—
219C2×#239—91no—
220C2×#239—181no—
221C2×#235—31no—
222C2×#235—91no—
223C3×C4×Q8—91no—
224C3×C4×D4—91no—
225Q8×Dic3—31no—
226#940—92no—
227#940—92no—
228#940—91no—
229#938—92no—
230#938—91no—
231#930—92no—
232#930—91no—
233#930—91no—
234#930—91no—
235#930—181no—
236C4×#67—31no—
237C4×#67—92no—
238#895—92no—
239#895—92no—
240#895—91no—
241#895—91no—
242#893—92no—
243#884—92no—
244#884—92no—
245#874—91no—
246#874—91no—
247#874—92no—
248#874—181no—
249C4×D12—31no—
250C4×D12—92no—
251C4×Dic6—31no—
252C23×C32—31no—
253C22×C3⋊D3—32no—
254C22×C3⋊D3—32no—
255C22×C3⋊D3—32no—
256C22×C3⋊D3—62no—
257C22×C3⋊D3—62no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—122no—
260C22×C3⋊D3C22×D312yes—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—32no—
264C22×C3×D3—32no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—61no—
268C22×C3×D3—62no—
269C22×C3×D3C22×D311yescharacteristic
270C22×C3×D3C22×D311yescharacteristic
271C32×Q8—34no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—31no—
276C2×C32×C4—32no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4—62no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284#638—122no—
285C2×C3⋊Dic3C22×D312yes—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C4⋊(C3⋊D3)—22no—
288C4⋊(C3⋊D3)—64no—
289C4⋊(C3⋊D3)—62no—
290C4⋊(C3⋊D3)—64no—
291C4⋊(C3⋊D3)—64no—
292C4⋊(C3⋊D3)—62no—
293C4⋊(C3⋊D3)—62no—
294C4⋊(C3⋊D3)—122no—
295C4⋊(C3⋊D3)—122no—
296C4⋊(C3⋊D3)—124no—
297C4⋊(C3⋊D3)—122no—
298C4×C3⋊D3—22no—
299C4×C3⋊D3—64no—
300C3×#67—64no—
301C3×#67—62no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3C22×D311yescharacteristic
313C2×C3×Dic3C22×D311yescharacteristic
314C2×C3×Dic3C22×D311yescharacteristic
315C2×C3×Dic3C22×D311yescharacteristic
316C2×C3×Dic3C22×D312yes—
317C2×C3×Dic3C22×D311yescharacteristic
318C2×C3×Dic3C22×D311yescharacteristic
319C2×C3×Dic3C22×D312yes—
320C3×D12—62no—
321C3×D12—64no—
322C3×D12—62no—
323C3×D12—62no—
324C3×D12—122no—
325C3×C4×D3—22no—
326C3×C4×D3—22no—
327C3×C4×D3—42no—
328C3×C4×D3—64no—
329C3×C4×D3—64no—
330C3×C4×D3—62no—
331C3×C4×D3—62no—
332C3×C4×D3—64no—
333C3×Dic6—24no—
334C3×Dic6D1214yescomplemented
335C3×Dic6#6714yescomplemented
336#626—22no—
337#626—24no—
338#626—68no—
339#626—64no—
340#626—64no—
341#626—64no—
342#626—64no—
343#626—124no—
344#626—122no—
345#626—122no—
346#626—124no—
347#626—122no—
348#626—122no—
349#626—122no—
350#626—122no—
351#626—124no—
352#625—122no—
353#624—24no—
354#624—68no—
355#624—64no—
356#624—64no—
357#550—271noSylow
358C2×C33C22×D411yescharacteristic
359C2×C33C2×#4111yescharacteristic
360C2×C33H(5,𝔽2)11yescharacteristic
361C3⋊(C3⋊D3)—42no—
362C3×C3⋊D3—41no—
363C3×C3⋊D3—42no—
364C32×D3—41no—
365C3×#41—184no—
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×Q8—61no—
369C2×C3×D4—92no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4—92no—
376C22×C3×C4—91no—
377C2×#67—32no—
378C2×#67—31no—
379C2×#67—92no—
380C2×#67—92no—
381C2×#67—92no—
382C2×#67—92no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—92no—
386C2×#67—182no—
387#239—64no—
388#239—184no—
389#239—184no—
390#239—188no—
391#235—64no—
392#235—184no—
393C2×D12—31no—
394C2×D12—32no—
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—61no—
398C2×D12—92no—
399C2×D12—92no—
400C2×D12—92no—
401C2×D12—92no—
402C2×D12—91no—
403C2×D12—91no—
404C2×D12—91no—
405C2×D12—92no—
406C2×D12—92no—
407C2×D12—92no—
408C2×D12—92no—
409C2×D12—181no—
410C2×D12—182no—
411C2×D12—181no—
412C2×D12—181no—
413C2×D12—182no—
414C2×D12—182no—
415C2×D12—361no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—61no—
421C2×C4×D3—92no—
422C2×C4×D3—92no—
423C2×C4×D3—92no—
424C2×C4×D3—182no—
425C2×C4×D3D3211yescharacteristic
426C2×Dic6D3211yescharacteristic
427C3×C4⋊C4—91no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C42—31no—
433C3×C42—31no—
434C3×C42—61no—
435C3×C42—92no—
436#217—31no—
437#217—92no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—92no—
443(C2×D3)⋊C4—92no—
444(C2×D3)⋊C4—92no—
445(C2×D3)⋊C4—92no—
446(C2×D3)⋊C4—182no—
447C4⋊Dic3—31no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—32no—
451C4⋊Dic3—61no—
452Dic3⋊C4—32no—
453Dic3⋊C4—31no—
454C4×Dic3—32no—
455C4×Dic3—32no—
456C4×Dic3D3211yescharacteristic
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—41no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32—61no—
464C22×C32C23×D311yescharacteristic
465C22×C32C23×D311yescharacteristic
466C22×C32C23×D311yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—62no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—62no—
476C2×C3⋊D3—62no—
477C2×C3⋊D3—62no—
478C2×C3⋊D3—62no—
479C2×C3⋊D3—62no—
480C2×C3⋊D3—62no—
481C2×C3⋊D3—62no—
482C2×C3⋊D3—62no—
483C2×C3⋊D3—122no—
484C2×C3⋊D3—122no—
485C2×C3⋊D3—124no—
486C2×C3⋊D3—122no—
487C2×C3⋊D3—122no—
488C2×C3⋊D3—122no—
489C2×C3⋊D3—122no—
490C2×C3⋊D3—122no—
491C2×C3⋊D3—122no—
492C2×C3⋊D3—242no—
493C2×C3⋊D3—242no—
494C2×C3×D3—22no—
495C2×C3×D3—21no—
496C2×C3×D3—21no—
497C2×C3×D3—21no—
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—21no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—62no—
504C2×C3×D3—61no—
505C2×C3×D3—62no—
506C2×C3×D3—62no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—61no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—62no—
513C2×C3×D3—62no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—121no—
517C2×C3×D3—121no—
518C2×C3×D3—122no—
519C2×C3×D3—122no—
520C2×C3×D3—122no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C32×C4—34no—
525C32×C4—32no—
526C32×C4—42no—
527C32×C4—61no—
528C32×C4—61no—
529C32×C4C2×D1212yes—
530C32×C4D3×D412yes—
531C32×C4C2×#6712yes—
532C3⋊Dic3—21no—
533C3⋊Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—21no—
537C3×Dic3—21no—
538C3×Dic3—21no—
539C3×Dic3—22no—
540C3×Dic3—24no—
541C3×Dic3—41no—
542C3×Dic3—62no—
543C3×Dic3—61no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—61no—
547C3×Dic3—122no—
548C3×Dic3C2×D1214yes—
549C3×Dic3#23512yescomplemented
550C3×Dic3#23912yescomplemented
551C3×Dic3C2×#6714yes—
552C2×#41—91no—
553C2×#41—271no—
554#127—271no—
555#127—272no—
556#121—272no—
557#121—272no—
558#121—271no—
559#121—271no—
560C4×Q8—91no—
561C4×D4—91no—
562C4×D4—272no—
563C33#55011yescharacteristic, complemented, Sylow
564C23×C3—31no—
565C23×C3—31no—
566C23×C3—61no—
567C23×C3—92no—
568C23×C3—91no—
569C22×D3—31no—
570C22×D3—31no—
571C22×D3—32no—
572C22×D3—32no—
573C22×D3—61no—
574C22×D3—62no—
575C22×D3—92no—
576C22×D3—92no—
577C22×D3—92no—
578C22×D3—182no—
579C22×D3—182no—
580C22×D3—182no—
581C22×D3—362no—
582C22×D3C2×D3211yescharacteristic
583C3×Q8—34no—
584C3×Q8—34no—
585C3×Q8—64no—
586C3×D4—182no—
587C3×D4—184no—
588C3×D4—182no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—32no—
594C2×C3×C4—31no—
595C2×C3×C4—32no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—41no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—62no—
604C2×C3×C4—61no—
605C2×C3×C4—62no—
606C2×C3×C4—62no—
607C2×C3×C4—92no—
608C2×C3×C4—91no—
609C2×C3×C4—122no—
610C2×C3×C4—184no—
611C2×C3×C4—182no—
612C2×C3×C4C2×D3211yescharacteristic
613C2×C3×C4C2×D3211yescharacteristic
614C2×C3×C4C2×D3211yescharacteristic
615#67—62no—
616#67—64no—
617#67—184no—
618#67—184no—
619#67—362no—
620#67—362no—
621#67—362no—
622#67—362no—
623#67—362no—
624#67—364no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—61no—
630C2×Dic3—62no—
631C2×Dic3C2×D3211yescharacteristic
632C2×Dic3C2×D3211yescharacteristic
633C2×Dic3C2×D3211yescharacteristic
634C2×Dic3C2×D3212yes—
635D12—62no—
636D12—64no—
637D12—62no—
638D12—62no—
639D12—122no—
640D12—184no—
641D12—184no—
642D12—184no—
643D12—184no—
644D12—184no—
645D12—188no—
646D12—182no—
647D12—182no—
648D12—182no—
649D12—362no—
650D12—362no—
651D12—364no—
652D12—364no—
653D12—362no—
654D12—362no—
655D12—364no—
656D12—362no—
657D12—362no—
658C4×D3—22no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—62no—
662C4×D3—62no—
663C4×D3—64no—
664C4×D3—184no—
665C4×D3—184no—
666C4×D3—188no—
667C4×D3—184no—
668Dic6#62614yescomplemented
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—121no—
682C2×C32C22×D1211yescharacteristic
683C2×C32C2×#23511yescharacteristic
684C2×C32C2×D3×D411yescharacteristic
685C2×C32C2×#23911yescharacteristic
686C2×C32D3×#4111yescharacteristic
687C2×C32#100911yescharacteristic
688C2×C32#100911yescharacteristic
689C2×C32#100911yescharacteristic
690C2×C32C22×#6711yescharacteristic
691C3⋊D3—41no—
692C3⋊D3—42no—
693C3⋊D3—122no—
694C3⋊D3—124no—
695C3⋊D3—122no—
696C3⋊D3—122no—
697C3⋊D3—242no—
698C3⋊D3—242no—
699C3⋊D3—244no—
700C3×D3—42no—
701C3×D3—41no—
702C3×D3—41no—
703C3×D3—122no—
704C3×D3—122no—
705C3×D3—122no—
706C3×D3—121no—
707C3×D3—121no—
708C3×D3—242no—
709#41—184no—
710#41—544no—
711C2×Q8—31no—
712C2×D4—91no—
713C2×D4—92no—
714C2×D4—91no—
715C2×D4—272no—
716C2×D4—272no—
717C2×D4—272no—
718C2×D4—272no—
719C2×D4—272no—
720C2×D4—271no—
721C22×C4—31no—
722C22×C4—92no—
723C22×C4—91no—
724C22×C4—272no—
725C4⋊C4—91no—
726C4⋊C4—92no—
727C4⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—91no—
730C22⋊C4—272no—
731C22⋊C4—272no—
732C42—31no—
733C42—92no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—62no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—182no—
748C22×C3—182no—
749C22×C3—182no—
750C22×C3—181no—
751C22×C3—181no—
752C22×C3—181no—
753C22×C3C22×D3211yescharacteristic
754C22×C3C22×D3211yescharacteristic
755C22×C3C22×D3211yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—122no—
775C2×D3—122no—
776C2×D3—122no—
777C2×D3—184no—
778C2×D3—182no—
779C2×D3—182no—
780C2×D3—182no—
781C2×D3—182no—
782C2×D3—182no—
783C2×D3—182no—
784C2×D3—182no—
785C2×D3—182no—
786C2×D3—182no—
787C2×D3—362no—
788C2×D3—362no—
789C2×D3—362no—
790C2×D3—362no—
791C2×D3—362no—
792C2×D3—362no—
793C2×D3—362no—
794C2×D3—362no—
795C2×D3—364no—
796C2×D3—722no—
797C2×D3—722no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—34no—
802C3×C4—32no—
803C3×C4—32no—
804C3×C4—34no—
805C3×C4—42no—
806C3×C4—64no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—61no—
810C3×C4—61no—
811C3×C4—61no—
812C3×C4—61no—
813C3×C4—121no—
814C3×C4—182no—
815C3×C4—181no—
816C3×C4D3×D1212yes—
817C3×C4C2×#62612yes—
818C3×C4D3×#6712yes—
819Dic3—21no—
820Dic3—21no—
821Dic3—62no—
822Dic3—61no—
823Dic3—62no—
824Dic3—62no—
825Dic3—61no—
826Dic3—122no—
827Dic3#379912yescomplemented
828Dic3C2×#62614yes—
829C32—21no—
830C32—21no—
831C32—21no—
832C32—41no—
833C32#555311yescharacteristic, complemented
834C32#557711yescharacteristic, complemented
835C32#583411yescharacteristic, complemented
836C23—31no—
837C23—91no—
838C23—92no—
839C23—272no—
840Q8—34no—
841D4—184no—
842D4—182no—
843D4—182no—
844D4—544no—
845D4—544no—
846D4—542no—
847D4—1082no—
848D4—1082no—
849D4—1082no—
850C2×C4—31no—
851C2×C4—32no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—62no—
855C2×C4—92no—
856C2×C4—91no—
857C2×C4—184no—
858C2×C4—182no—
859C2×C4—544no—
860C2×C4D3311yescharacteristic
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—122no—
874C2×C3—121no—
875C2×C3—121no—
876C2×C3—361no—
877C2×C3—362no—
878C2×C3C2×#379911yescharacteristic
879C2×C3C2×D3×D1211yescharacteristic
880C2×C3D3×#23511yescharacteristic
881C2×C3#6430811yescharacteristic
882C2×C3#6430811yescharacteristic
883C2×C3D3×#23911yescharacteristic
884C2×C3#6432011yescharacteristic
885C2×C3C22×#62611yescharacteristic
886C2×C3C2×D3×#6711yescharacteristic
887D3—41no—
888D3—122no—
889D3—122no—
890D3—121no—
891D3—121no—
892D3—122no—
893D3—242no—
894D3—364no—
895D3—362no—
896D3—362no—
897D3—362no—
898D3—722no—
899D3—722no—
900D3—724no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—181no—
905C22—182no—
906C22—181no—
907C22—182no—
908C22—182no—
909C22—181no—
910C22—542no—
911C22—542no—
912C22—542no—
913C22C2×D3311yescharacteristic
914C4—32no—
915C4—34no—
916C4—61no—
917C4—61no—
918C4—182no—
919C4—181no—
920C4D3×#62612yes—
921C3—21no—
922C3—21no—
923C3—21no—
924C3—41no—
925C3#1059390211yescharacteristic, complemented
926C3#1059500711yescharacteristic, complemented
927C3#1059541011yescharacteristic, complemented
928C2—121no—
929C2—361no—
930C2—362no—
931C2—1082no—
932C2D3×#379911yescharacteristic
933C2#1172439011yescharacteristic
934C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#550
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#89018C2semidirect
2. C2×C3×#3799C2semidirect
3. #11723696C2semidirect
4. #11723517C2semidirect
5. #11723516C2semidirect
6. C3×C4×#626C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723030C2semidirect
9. #11722963C2semidirect
10. #11722961C2semidirect
11. #11722933C2semidirect
46. C2×#3799D3semidirect
73. C4×#626D3semidirect
75. Dic3×Dic6D3semidirect
91. C32×Dic6D4semidirect
215. C32×Dic3#41semidirect
334. C3×Dic6D12semidirect
335. C3×Dic6#67semidirect
549. C3×Dic3#235semidirect
550. C3×Dic3#239semidirect
563. C33#550semidirect
668. Dic6#626semidirect
827. Dic3#3799semidirect
833. C32#5553semidirect
834. C32#5577semidirect
835. C32#5834semidirect
925. C3#10593902semidirect
926. C3#10595007semidirect
927. C3#10595410semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#890182
C2×C3×#37992
#117236962
#117235172
#117235162
C3×C4×#6262
C3×Dic3×Dic62
#117230302
#117229632
#117229612
#117229332
#105954103
#105950073
#105939023